Originally you said you wanted to shave enough power usage off to get below the next electrical bill tier increase.
First of all, how much are you over the limit are you? How much do you need to shave off? How much are you saving by getting below that limit? If you're going to spend a thousand bucks on solar stuff to save $50/mo, and only during AC season, you may never get a return on investment by buying solar equipment. Having solid data will also tell you how much power you need to generate or save to make this whole endeavor worth doing at all.
You're limited in what you can do by being in a rental, but if I was in your situation, I'd look long and hard at reducing my existing usage before I looked at generating anything. As the old saying goes, it's easier to save a watt than generate a watt.
Here are a pile of ideas, no particular order, just as they came to mind. Most of this is pretty old school:
Do you have blackout curtains? There are insulated curtains, and also window films which can reduce solar infiltration - same idea as tinted windows on your car.
Turn off the dang lights and TV when no one is in the room. Even with LED bulbs, if leaving them on costs you $2/mo, and you normally wouldn't care about the $2, if getting under that billing tier is the main goal, then this all adds up. Some TVs burn a surprising amount of power, even if they're flat screen.
Turn off your computer and your 12 monitors when you're not using it.
Put as many wall warts and chargers as you can on power strips, and turn them all off when not in use.
Do your doors have good seals around them? A $30 IR thermometer can help you find air leaks. Fixed with as simple as a rolled up towel on the floor, or as proper as installing a new threshold and weather stripping.
If you cook with an old school resistance electric cooktop, look at an induction plug-in hot plate and use that as much as you can. As well as being more efficient itself, it'll also reduce the load on your AC system, saving more power. Force multiplier.
If you boil a lot of water, drink a lot of tea or something, look at a self contained electric kettle vs. boiling water on the stove. Much more efficient than a stovetop burner, also cuts load on the AC system. If you are boiling a kettle on the stove, cool it down with cold water when you're done, so that heat isn't radiating into the house, making the AC work harder.
Can you use the super efficient window AC you're talking about, and only AC the room or rooms you're occupying? My parents used to heat the living room with a wood stove, and hung a sheet between the living room and the rest of the house to keep the heat in the room we were occupying. Same idea could apply here.
Cook outside during AC season. If you're simmering a stew, put it in a crockpot on your back porch. Don't dump all that heat into your house, where your AC then has to work to pull it out of the house. Same thing with sous vide. Use your induction hot plate and take it outside. I do this when frying fish or making curry anyway, otherwise the house smells like curry for a week afterwards. Dump your hot sous vide water and cool the container down with cool water, don't let all the heat radiate into the house for the AC to then remove.
Use the old-school pre-AC cooling method when you can, open up your house at night and run fans to vent the heat. Close it up in the morning, before the heat of the day. No clue where you live, if it's still 90F at midnight this obviously won't be an option.
Talk to your landlord, they might be onboard with you making other changes as well. Water heater blanket, extra attic insulation, timer on the water heater, etc.
Get the data first, though.